Question

A bond has a face value and redemption value of $140. It pays coupons annuallt at an effective annual rate that is the double of th effetive annual yield. The present value of the remdeption amount is 3 times the present value of the coupon stream. What is the price of the bond?

Answer: $160.... Please show working out

Answer 1

Let r be effective annual yield
then 2r is the annual effective coupon yield. Coupon = Face Value * 2r
The present value of the remdeption amount is 3 times the present value of the coupon stream.
PV of Face Value = 3* Pv of Coupon stream
Hence Face Value /(1+r) =3 * Face Value * 2r/(1+r)
1000/(1+r) = 3* 1000 *2r /(1+r)
Hence r = 1/6 or 16.67%
Price of Bond = face Value/(1+r) + Coupon /(!+r) = 1000/(1 +1/6) + (1000 *2 *1/6)/(1+1/6) = 120 + 40 = 160

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